Yes. Verbal contracts are valid contracts, but difficult to enforce in court because of a lack of evidence. You can also write something and have the other person sign it. Remember that it does cost money to file a breach of contract complaint if you have to take them to court.
A verbal would work but hard to prove. It would be best just to type or write something up, be specific as possible and include dates. Have that person sign it and ta da! That's your legal contract. If for some reason they don't pay, you can take them to court for it.